Yes, you did the right thing if you would like messages addressed to that number relayed to your Mac. On your phone, there is a setting to allow messages to be shared with your other device (s), which needs to be on.

Yes, as above it means you will receive messages on your Mac when sent to your phone number. They will also still go to your phone. All my messages go to all my devices so it doesn't matter what I'm sitting with I can receive and answer all my messages

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